Reliability and the Theory of Interference

There are two aspects of reliability in reverse engineering. Reliability in statistics refers to the consistency or repeatability of a measurement. It relies on the repeatability of the same measurement instrument, and the comparability of similar measurement instruments. It also depends on the repeatability of the operator of the test machine or the device. It does not imply the validity of the data that reflect whether the test result or measurement is what was intended to be obtained. A misaligned Rockwell hardness tester will repeatedly produce consistently biased hardness data. Statistically, the measurement by this tester is of high reliability despite it is not producing valid engineering data. 

The second aspect of reliability is referred to as part functionality. The reliability of a part reflects the probability that this part will perform a required function without failure under stated conditions for a stated period of time. Reliability of a part analyzes time to event. Statistically, failure of a part is deemed as a sample event. The objective is to predict the rate of events for a given population (often referred to as failure rate or hazard rate) or the probability of an event for an individual part. Part reliability plays a crucial role in machine design, and in reverse engineering that reinvents the same part. It is an important continued operational safety issue, and also has a significant financial impact because it helps to predict the probability of failure for a part over a period of time. 

The reliability theory is heavily dependent on statistics and probability, but was developed apart from mainstream statistics and probability to help insurance companies in the nineteenth century. It also heavily relies on the theory of interference. Part fimctional reliability will be discussed below in terms of safety margins and Weibull analysis. 

In the following example, a shaff made of steel is reverse engineered. A total of thirty parts are analyzed, and the test data show that their tensile strength has a normal distribution with a mean of 650 MPa and a standard deviation of 10 MPa. This part will be subjected to a tensile stress in service that fluctuates in a normal distribution pattern, with a mean of 550 MPa and a standard deviation of 20 MPa. Therefore, 

All the material properties, such as tensile strength and fatigue endurance, can be presented as statistical data. All the loads externally applied to the part can also be represented as statistical data. The above example indicates that a simple conclusion on safety can easily be reached using the conventional deterministic mechanics that only applies a singular value in its calculation. However, when reliability in terms of a quantitative percentage is required.  

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